I have a Lenovo ThinkCentre running Windows 10. Graphics card is an Intel Q45/Q43 Express Chipset. Main display is connected via VGA. Second monitor is connected via DVI to DisplayPort w/adapter.

Drivers are updated. I've tried disconnecting the monitor from VGA and booting the computer with a single monitor connected to the DisplayPort and it doesn't work at all. I'm not sure if there's a BIOS setting I can update, or if there's a problem with the DisplayPort, or what. No matter what I do, it won't detect the 2nd monitor. I'm considering just buying a splitter for the VGA port but I feel like there should be a way to get this working without using a splitter.

I'm still confused. My machine is currently running Windows 10 and I have one monitor connected and working perfectly. I am probably missing something due to my inexperience but your answer isn't clarifying anything for me.

The Q45/Q43 is very old and comes under the category of "legacy" graphics. Intel is not providing an updated driver for Windows 10. What you are using is the Microsoft generic driver, which seems to be providing what you need for one monitor.